Answer to Question #323838 in Statistics and Probability for Bless

Question

 You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let N be the number of times the two dice have to be rolled before the game is decided.

(a) Determine the probability mass function of N.

(b) Compute E[N].

(c) Compute P(you win).

(d) Assume that you get paid $10 for winning in the first round, $1 for winning in any other round, and nothing otherwise. Compute your expected winnings.